Sign-changing solutions for a fractional Schrodinger-Poisson system

In this paper, we deal with the existence and multiplicity of radial sign-changing solutions for fractional Schrodinger-Poisson system: {(- Delta)(s)u + u + phi u = f (u), (- Delta)(alpha) phi = u(2), in R-3 (P) where s is an element of (3/4, 1), alpha is an element of (0, 1) and f is a continuous function. Based on perturbation approach and the method of invariant sets of descending flow, we obtain the existence and multiplicity of radial sign-changing solutions of system (P). In addition, by applying the constrained variational method incorporated with Brouwer degree theory, we prove that system (P) possesses at least one radial ground state sign-changing solution. Furthermore, we show that the least energy of sign-changing solutions exceed twice than the least energy, and when f is odd, system (P) admits infinitely many nontrivial solutions.